seems we go through this topic 1-2 X /year....for a general look at various cleaning methods:
Best camera lens cleaners in 2020 | Digital Camera World
Carbon tipped lens type designs will not scratch your camera lens or glasses. But it depends if there are any larger foreign substances on the lenses, in which case rubbing the lens surface will scratch. So blow off dirt first, then clean. The carbon attracts the oil and dirt, then you recharge the tip with more carbon for the next time. The only problem we found in our office using the device, the applicator tip only covers a few mm so you need to go in a circular pattern all over the lens, time consuming, then check the lens as you may have missed some overlapping areas. Sam eproblem we noticed when cleaning lenses in glasses. Sales rep, who we know very well, told us we were the only one having these problems.
Microfibre cloths are usually included with camera bodies, all lenses, and even with $50k eye imaging equipment. The synthetic fibres are smooth and fine enough to not scratch lenses and absorb the oil and films. Again, larger particles need to be blown off forst. Eventually the cloth absorbs too much foreign material and does not clean properly. At that point, the cloth is to be thrown out. Cleaning these type of cloths will result in the fibres becoming looser and possibly scratching a lens. The larger and thicker cloths used for i.e. cleaning a TV screen have larger diameter fibres and can be washed and reused. So generally for cleaning cameras or glasses, use lens cleaner on cloth, clean, use a dry part of the cloth to finish drying.
Lens paper is so finely made that when wet it will not scratch and the alcohol applied chemical will evaporate by itself.
A shirt, silk scarf, etc., may feel soft but the rough edges of the fibres will eventually scratch your lenses. Which is why you will notic lots of fine scratches on patient's glasses when that is how they clean them.
Best source now for all the necessary items, just like almost everything else, Amazon.